Time-consistent decisions and rational expectation equilibrium existence in DSGE models

October 23, 2019

By Minseong Kim


We demonstrate that if all agents in an economy make time-consistent decisions and policies, then there exists no rational expectation equilibrium in a dynamic stochastic general equilibrium (DSGE) model, unless under very restrictive and special circumstances. Some time-consistent interest rate rules, such as Taylor rule, worsen the equilibrium non-existence issue in general circumstances. Monetary policy needs to be lagged in order to avoid equilibrium non-existence due to agents making time-consistent decisions. We also show that due to the transversality condition issue, either fiscal-monetary coordination may need to be modeled, or it may be necessary to write a model such that bonds or money provides utility as medium of exchange or has liquidity roles.

This is one of those rare papers where you start thinking: “Really? How has everybody missed this for so long?” This seems to be a quite fundamental issue and I am eager to see how others react to it.

Can We Save the American Dream? A Dynamic General Equilibrium Analysis of the Effects of School Financing on Local Opportunities

October 19, 2019

Fabian Eckert and Tatjana Kleineberg


Neighborhoods in the US differ substantially in the educational and economic opportunities that they offer to children who grow up in them. We develop and estimate a structural spatial equilibrium model of residential and education choice to study the effects of school financing policies on education outcomes, intergenerational mobility, and welfare at the local and aggregate level. Our model generates persistent effects of children’s neighborhoods on adult outcomes through local labor market access and local human capital formation. Local school funding is an important component of the latter. Schools are funded through income taxation and local rent taxation. We estimate the model using a range of US Census datasets by fitting model predictions to regional data of the actual US geography. We use the estimated model to study the effects of counterfactual policy interventions, in particular, the equalization of school funding across all students and the use of rent subsidies. We find that general equilibrium responses in local prices and local skill compositions significantly dampen the partial equilibrium effects of the policy, so that effects on education outcomes and intergenerational mobility are positive but only moderate in general equilibrium.

I find the result of this very good paper very disappointing. There is a sense that a lot of Einsteins are missed because of the uneven distribution of school funding in the United States. This paper shows that education remains mostly prohibitive for the poor if you centralize school funding. This is because their neighborhoods become more expensive.

Optimal Fiscal Policy without Commitment: Beyond Lucas-Stokey

October 19, 2019

By Davide Debortoli, Pierre Yared and Ricardo Nunes


According to the Lucas-Stokey result, a government can structure its debt maturity to guarantee commitment to optimal fiscal policy by future governments. In this paper, we overturn this conclusion, showing that it does not generally hold in the same model and under the same definition of time-consistency as in Lucas-Stokey. Our argument rests on the existence of an overlooked commitment problem that cannot be remedied with debt maturity: a government in the future will not tax on the downward slopping side of the Laffer curve, even if it is ex-ante optimal to do so. In light of this finding, we propose a new framework to characterize time-consistent policy. We consider a Markov Perfect Competitive Equilibrium where a government reoptimizes sequentially and may deviate from the optimal commitment policy. We find that, in a deterministic economy, any stationary distribution of debt maturity must be flat, with the government owing the same amount at all future dates.

I must confess I have a hard time wrapping my head around this paper. My difficulty lies in the example that it provides: why would it ever be ever ex-ante optimal for a government to tax on the downward-sloping side of the Laffer curve? The entire point of the Laffer curve is that you do not want to be there.

Bad Jobs and Low Inflation

October 19, 2019

Renato Faccini and Leonardo Melosi


Since 2014 the U.S. economy has been characterized by (i) a tight labor market with a record-low unemployment rate and very high job finding rates, (ii) disappointing labor productivity growth, and (iii) low inflation. We propose a model with the job ladder that can reconcile these three facts. In the model inflation picks up only when most jobs are concentrated at the high rung of the ladder: as firms compete for efficiently allocated employed workers, outside offers are declined and matched, triggering an increase in production costs that is not backed by an increase in productivity. The model is estimated using unemployment and quit rates, which allow the model to precisely identify the distribution of the quality of jobs. After the Great Recession, the observed structural drop in the job-to-job rate has slowed down the pace at which the U.S. labor market turns bad jobs into good jobs. As a result, inflation has not escalated even though the labor market appears to be very tight. Furthermore, the model predicts that labor productivity persistently fell by up to 70 bps in the post-Great Recession recovery owing to this protracted misallocation in the labor market.

This paper addresses an important question that is puzzling many in an elegant way. However, I am still left hungry: what triggered that change in job-to-job transitions that is taken exogenously here?

Health Risk, Insurance and Optimal Progressive Income Taxation

October 10, 2019

By Juergen Jung and Chung Tran


We study the optimal progressivity of personal income taxes in an environment where individuals are exposed to idiosyncratic shocks to health and labor productivity over the lifecycle. Our analysis is based on a large-scale overlapping generations general equilibrium model that is calibrated to the US economy. Our results indicate that the presence of health risk and health insurance has a strong effect on the amount of redistribution and social in- surance provided by progressive income taxes. In an environment with a non-universal health insurance system, such as the US system, the optimal income tax system is highly progressive in order to provide a sufficient level of redistribution to unhealthy low income individuals. The total welfare gain from optimizing the progressivity level is 5.6 percent in compensating lifetime consumption. More inclusive health insurance systems, such as Medicare for all, lead to large decreases in the optimal level of tax progressivity. When health expenditure risk is eliminated, the optimal income tax code becomes more similar to the findings of previous studies that used models without health risk. Our findings highlight the quantitative importance of accounting for the interdependence of health insurance and income taxes when designing optimal income tax policies.

There is quite a bit of discussion these days on the progressivity of US taxes. When comparing it to other countries, and possibly across time as well, it is important to also consider the impact of government benefits as well. On top of that, this paper shows that health insurance coverage is a major factor as well. This is indeed a complicated question.

Rational Inattention and Oversensitivity of Retirement to the State Pension Age

October 10, 2019

By Jamie Hentall MacCuish


This paper presents evidence that incorporating costly thought, modelled with rational inattention, solves two well-established puzzles in the retirement literature. The first puzzle is that, given incentives, the extent of bunching of labour market exits at legislated state pension ages (SPA) seems incompatible with rational expectations (e.g. Cribb, Emmerson, and Tetlow, 2016). Adding to the evidence for this puzzle, this paper includes an empirical analysis focusing on whether liquidity constraints can account for this bunching and finds they cannot. The nature of this puzzle is clarified by exploring a life-cycle model with rational agents that does match aggregate profiles. This model succeeds in matching these aggregates only by overestimating the impact of the SPA on poorer individuals whilst underestimating its impact on wealthier people. The second puzzle is that people are often mistaken about their own pension provisions (e.g. Gustman and Steinmeier, 2001). Concerning this second puzzle, I incorporate rational inattention to the SPA into the aforementioned life-cycle model, thus allowing for mistaken beliefs. To the best of my knowledge, this paper is the first to incorporate rational inattention into a life-cycle model. Rational inattention not only improves the aggregate fit of the data but better matches the response of participation to the SPA across the wealth distribution, hence simultaneously offering a resolution to the first puzzle. This paper researches these puzzles in the context of the ongoing reform to the UK female state pension age

As the population ages and pension systems adapt, there will be more confusion about the “correct” age to retire. As the paper shows, there is in fact already quite a bit of confusion about this in the UK. It is important to understand this to see the consequences on retirement choices. Plus it is interesting to see the application of rational inattention in a life-cycle model.

Heterogeneous Price Rigidities and Monetary Policy

October 10, 2019

By Christopher Clayton, Andreas Schaab and Xavier Jaravel


This paper investigates the implications of heterogeneous price rigidities across sectors for the distributional and aggregate effects of monetary policy. First, we identify and characterize analytically a new set of earnings and expenditure channels of monetary policy that emerge in the presence of sectoral heterogeneity. Second, we establish empirically that (i) prices are more rigid in sectors selling to college-educated households, (ii) prices are more rigid in sectors employing college-educated households, and (iii) sectors that employ college-educated households also sell more to these households. These new facts suggest that monetary policy stabilizes sectors that matter relatively more for college-educated households, due to an expenditure channel (from (i)), an earnings channel (from (ii)), and their amplification by feedback loops (from (iii)). Finally, we develop a multi-sector incomplete-markets Heterogeneous Agent New Keynesian model, in which households of different education levels work and consume in different sectors. We quantify the aggregate and distributional effects from heterogeneous price rigidities using this model. In the baseline calibration, we find that the consumption of college-educated households is 22% more sensitive to monetary policy shocks as that of non-college households, while the aggregate real effect of monetary policy is 5% stronger than with homogeneous price rigidities.

The usual way to look at the distributional impact of monetary policy is too study types of household as they differ on income, assets or sector they work in. That paper takes a novel approach: the price rigidity differs by type of goods, and different types of households have different consumption baskets. Intriguing.